The exact Schur index of N = 4 SYM

Jun Bourdier*, Nadav Drukker, Jan Felix

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)
173 Downloads (Pure)


The Witten index counts the difference in the number of bosonic and fermionic states of a quantum mechanical system. The Schur index, which can be defined for theories with at least N=2 supersymmetry in four dimensions is a particular refinement of the index, dependent on one parameter q serving as the fugacity for a particular set of charges which commute with the hamiltonian and some supersymmetry generators. This index has a known expression for all Lagrangian and some non-Lagrangian theories as a finite dimensional integral or a complicated infinite sum. In the case of N=2 SYM with gauge group U(N) we rewrite this as the partition function of a gas of N non interacting and translationally invariant fermions on a circle. This allows us to perform the integrals and write down explicit expressions for fixed N as well as the exact all orders large N expansion.

Original languageEnglish
Article number210
Pages (from-to)1-10
Number of pages10
JournalJournal of High Energy Physics
Issue number11
Publication statusPublished - 30 Nov 2015


  • Matrix Models
  • Supersymmetric gauge theory


Dive into the research topics of 'The exact Schur index of N = 4 SYM'. Together they form a unique fingerprint.

Cite this